As with the Silver and Gold Tournament suggestions, hold this off until the end. You have to complete the other three tournaments anyway to get to this point, but they shouldn't be too difficult if you've waited until the end of the game and then converted the Difficulty to Casual. In fact, you should breeze right through it. The only thing that will cause any problem is the final fight, where you fight the Hydra and the War Thog (or whatever it's called) together in the same arena fight. The same strategies that took care of them before will work this time as well. For the big gorilla, I used the saws to quickly take its life down every time, and the Liberator seemed to work decent against the Hydra Just take care of both of them and then you will have this trophy.
*NOTE: Round 4 of this tournament will reward you with the Treasure Map, which will actually help you with:
With that item, you can actually see them on your map (when on a planet, not a planetoid).